 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...parallel DE would be divided also into equal parts at the points 7J K, L. PROPOSITION XXIII. THEOEEM. In a right-angled triangle, if a perpendicular is...the vertex of the right angle to the hypothenuse. \st. The triangles on each side of the perpendicular are similar to the whole triangle, and to each... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...parallel DE would be div'ded also into equal parts at the points I, K, L. PROPOSITION XXIII. THEOREM. In a right•angled triangle, if a perpendicular is...the vertex of the right angle to the hypothenuse. 1st. The triangles on each side of the jxrpendicular are similar to the given triangle, and to each... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...parallel DE would be divided also into equal parts at the points I, K, L. PROPOSITION XXIII. THEOREM. In a right•angled triangle, if a perpendicular is...the vertex of the right angle to the hypothenuse. 1st. The triangles on each side of the perpendicular are similat to the given triangle, and to each... | |
 | Charles Davies, William Guy Peck - Mathematics - 1857 - 608 pages
...be drawn to (he vertices of the triangle ; then AN x BL X CM = AM X CL x BN. 14. In a right angled triangle, if a perpendicular is drawn from the vertex of the right angle to the hypothenuse, 1st. The triangles formed are similar to each other and to the whole triangle. 2d. Either side about... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...would also be divided into equal parts at the points I, K, L. PROPOSITION XXVII. — THEOREM. 269. In a right-angled triangle, if a perpendicular is...vertex of the right angle to the hypothenuse, the triangle will be divided into two triangles similar to the given triangle atul to each other. In the... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...A~B2 : : BC : B D. In like manner, we have, BTP : AC2 : : BC : C D. 240. Cor. 3. If a perpendicular be drawn from the vertex of the right angle to the hypothenuse, the squares of the sides about the right angle will be to each other as the adjacent segments of the hypothenuse.... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...ABa : : BC : B D. In like manner, we have, FC2 : ACa : : BC : C D. 240. Cor. 3. If a perpendicular be drawn from the vertex of the right angle to the hypothenuse, the squares of the sides about the right angle will be to each other as the adjacent segments of the hypothenuse.... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...: : BC : B D. In like manner, we have, B~C3 : A~C2 : : BC : C D. 240. Cor. 3. If a perpendicular be drawn from the vertex of the right angle to the hypothenuse, the squares of the sides about the right angle will be to each other as the adjacent segments of the hypothenuse.... | |
 | Charles Davies, William Guy Peck - Mathematics - 1865 - 592 pages
...vertices of the triangle ; the» AN x HI, x CM = AM x CL x BN. 14.' In a right angled triangle, if л perpendicular is drawn from the vertex of the right angle to the hypothenuse 1st. The triangles formed are similar to each other and to the whole triangle. 2d. Either side about... | |
 | Benjamin Greenleaf - Geometry - 1866 - 328 pages
...would also be divided into equal parts at the points I, K, L. PROPOSITION XXVII. — THEOREM. 269. In a right-angled triangle, if a perpendicular is drawn from the vertex of the right angle to the hypothe«tt.se, the triangle will be divided into two triangles similar to the given triangle and to... | |
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If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. 
